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File:Lda-gauss-1.svg

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Original file(SVG file, nominally 899 × 543 pixels, file size: 56 KB)

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Summary[edit]

Description
English: Normal distribution for a discriminant analysis
Deutsch: Normalverteilung bei einer Diskriminanzalayse
 
 
Date
Source Own work
Author MartinThoma
 
W3C-validity not checked.

Source is available at github

LaTeX Code[edit]

\documentclass[varwidth=true, border=5pt]{article}
\usepackage[active,tightpage]{preview}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning} 
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\pgfmathdeclarefunction{gauss}{2}{%
  \pgfmathparse{1/(sqrt(2*pi*#2))*exp(-((x-#1)^2)/(2*#2))}%
}
% to be used: \gauss(mean)(variance)

\pgfplotsset{
tick label style = {font=\sansmath\sffamily},
every axis label/.append style={font=\sffamily\footnotesize},
}

% Thanks to percusse for solving problems with the axis

\begin{document}
\begin{preview}
\tikzstyle{plotA}=[ultra thick,red!90!black]
\tikzstyle{plotB}=[ultra thick,cyan!50!black]
\begin{tikzpicture}
    \begin{axis}[
        width=13.5cm,
        height=8.625cm,
        % Grid
        grid = major,
        % size
        xmin= 0,     % start the diagram at this x-coordinate
        xmax= 125,   % end   the diagram at this x-coordinate
        ymin= 0,     % start the diagram at this y-coordinate
        ymax= 0.045, % end   the diagram at this y-coordinate
        % Legende
        legend style={
            font=\large\sansmath\sffamily,
            at={(0.5,-0.18)},
            anchor=north,
            legend cell align=left,
            legend columns=-1,
            column sep=0.5cm
        },
        % Ticks
        tick align=inside,
        minor tick style={thick},
        scaled y ticks = false,
        xtick={40,70,80},
        ytick=\empty,
        % Axis
        axis on top,
        axis line style = {very thick,shorten <=-0.5\pgflinewidth},
        axis lines = middle,
        axis line style = very thick,
        xlabel=$x$,
        x label style={at={(axis description cs:0.5,0)},
                       anchor=north,
                       font=\boldmath\Large},
        ylabel=$f(x)$,
        y label style={at={(axis description cs:0,0.5)},
                       anchor=south,
                       rotate=90,
                       font=\boldmath\Large},
        ]

        \coordinate (plotAcoord) at (axis cs:70,0.024);
        \coordinate (plotAcoordY) at (axis cs:0,0.024);
        \draw[plotA,thick, dashed](plotAcoord -| plotAcoordY) -- (plotAcoord);

        \coordinate (plotBcoord) at (axis cs:70,0.0004);
        \coordinate (plotBcoordY) at (axis cs:0,0.0004);
        \draw[plotB,thick, dashed](plotBcoord -| plotBcoordY) -- (plotBcoord);

        \node[above right=0cm and 0cm of plotAcoordY,color=red!90!black] (f1y) {$f_{I}(70)$};
        \node[above right=0cm and 0cm of plotBcoordY,color=cyan!50!black] (f2y) {$f_{II}(70)$};

        % Plots of the distributions
        \addplot [domain=0:120,samples=200,plotA] {gauss(80,100)};
        \addplot [domain=0:120,samples=200,plotB] {gauss(40,100)};

        % Mark points
        \addplot+[plotA,
                  samples at={70},
                  mark=*,
                  mark options={scale=1, fill=red!90!black}] {gauss(80,100)};
        \addplot+[plotB,
                  samples at={70},
                  mark=*,
                  mark options={scale=1, fill=cyan!50!black}] {gauss(40,100)};
        \coordinate (a) at (axis cs:70,0.024);
        \draw[black,thick](a |- current plot begin) -- (a);

        % Add labels
       \node[plotA,above] at (axis cs:102,0.03){\Large $\mathcal{N}(80, 100)$};
       \node[plotB,above] at (axis cs:20,0.03){\Large $\mathcal{N}(40, 100)$};
      % \addlegendentry{$\mu=80,\enskip \sigma^2 = 100$}
      % \addlegendentry{$\mu=40,\enskip \sigma^2 = 100$}
    \end{axis} 
\end{tikzpicture}
\end{preview}
\end{document}

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

This image has been assessed using the Quality image guidelines and is considered a Quality image.

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File history

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Date/TimeThumbnailDimensionsUserComment
current02:34, 19 August 2014Thumbnail for version as of 02:34, 19 August 2014899 × 543 (56 KB)MartinThoma (talk | contribs)Improved axis
01:53, 19 August 2014Thumbnail for version as of 01:53, 19 August 2014899 × 543 (56 KB)MartinThoma (talk | contribs)Dashed horizontal lines
14:07, 18 August 2014Thumbnail for version as of 14:07, 18 August 2014899 × 543 (56 KB)MartinThoma (talk | contribs)Put labels to ordinates
10:46, 14 August 2014Thumbnail for version as of 10:46, 14 August 2014899 × 543 (56 KB)MartinThoma (talk | contribs)Nicht <math>f(x_0) = 70</math>, sondern <math>f(70)</math>.
17:28, 12 August 2014Thumbnail for version as of 17:28, 12 August 2014899 × 543 (64 KB)MartinThoma (talk | contribs)Labels für die Verteilungen (N(40,100) und N(80,100)) vergrößert
17:23, 12 August 2014Thumbnail for version as of 17:23, 12 August 2014899 × 543 (63 KB)MartinThoma (talk | contribs)Rahmen entfernt; Punkte auf Plots bei x=70 sind nun gefüllt
17:14, 12 August 2014Thumbnail for version as of 17:14, 12 August 2014899 × 571 (63 KB)MartinThoma (talk | contribs)Vorschläge von Sigbert umgesetzt
03:59, 12 August 2014Thumbnail for version as of 03:59, 12 August 2014900 × 593 (86 KB)MartinThoma (talk | contribs)Marked x=70 for both distributions
17:46, 11 August 2014Thumbnail for version as of 17:46, 11 August 2014900 × 593 (74 KB)MartinThoma (talk | contribs){{Information |Description ={{en|1=Normal distribution for a discriminant analysis}} {{de|1=Normalverteilung bei einer Diskriminanzalayse}} |Source ={{own}} |Author =MartinThoma |Date =2014-08-11 |Permi...

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